Archive for Mathematical Logic

, Volume 48, Issue 6, pp 551–577 | Cite as

Deep sequent systems for modal logic

  • Kai BrünnlerEmail author


We see a systematic set of cut-free axiomatisations for all the basic normal modal logics formed by some combination the axioms d, t, b, 4, 5. They employ a form of deep inference but otherwise stay very close to Gentzen’s sequent calculus, in particular they enjoy a subformula property in the literal sense. No semantic notions are used inside the proof systems, in particular there is no use of labels. All their rules are invertible and the rules cut, weakening and contraction are admissible. All systems admit a straightforward terminating proof search procedure as well as a syntactic cut elimination procedure.


Nested sequents Modal logic Cut elimination Deep inference 

Mathematics Subject Classification (2000)

03F05 03B45 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für AngewandteMathematik und InformatikBernSwitzerland

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